We can now take into consideration the equations one by one, starting from the continuity constrain. A detailed treatment for what concerns fluid flows equations discretization, the interested reader can refer to [1]}. The equation can be written into its integral form over each cell as follows:
\(\int _{\Omega _i} \nabla \cdot \left( \overline{\rho } \tilde{\mathbf {u}} \right) dV = 0.\) 
